1. Field of the Invention
The present invention relates to signal processing. More particularly, the present invention relates to efficient and accurate filtering and interpolation techniques for discrete time input signals.
2. Related Art
Many industrial processes involve motion along trajectories that are defined by precise positions at specific times. Photolithography is an example of such a process. In a photolithography process, an illumination source projects an illumination beam. The beam passes through, or is reflected off, a reticle to enable the transfer of a reticle image from the reticle to a substrate, such as a semiconductor wafer.
Scanning techniques are employed in photolithography processes to project a reticle image onto a substrate. These scanning techniques involve moving a reticle across an illumination slot to allow the reticle image to be exposed onto a substrate that is simultaneously moving. Reticles and substrates are disposed on stages that are capable of motion in one or more dimensions.
To provide precise movement in such processes, automated command and control systems are needed. These command and control systems often employ signal processing techniques to govern these processes. However, signal processing techniques can be computationally expensive and slow. In addition, processing platforms, such as microcontrollers, that implement such techniques can introduce unacceptable computational errors. Accordingly what is needed are signal processing techniques for such systems that induce minimal computational errors, require a minimal number of processing operations, and execute in a minimal amount of time.
The present invention is directed to efficient and accurate interpolation techniques. A method of the present invention reduces the number of operations required to interpolate a discrete input signal having a first sampling rate into a discrete output signal having a second sampling rate. This method includes selecting a plurality of input signal values from the input signal, wherein each selected input signal value corresponds to a particular time increment at the first sampling rate; and generating, at a time increment occurring at the second sampling rate, an output signal value. The step of generating the output signal value includes calculating an inner product of the plurality of input signal values and a corresponding plurality of filter response function values, and summing the inner product with a prior time increment output signal value.
The generating step can be repeated for multiple time increments occurring at the second sampling rate. This repetition produces a corresponding set of discrete output signal values.
A further method of the present invention accurately processes a discrete time input signal having a first clock rate into a discrete time output signal having a second clock rate with minimal computational errors. This method includes delta filtering the input signal to produce an intermediate signal having the first clock rate, and delta interpolating the intermediate signal to produce the output signal.
Delta filtering includes calculating an input delta signal by subtracting an initial value from the input signal, generating a filtered delta signal, and adding the initial value to the filtered delta signal. Delta interpolating includes upsampling the intermediate signal to the second clock rate, calculating an upsampled intermediate delta signal by subtracting an initial value from the upsampled intermediate signal, filtering the intermediate delta signal, and adding the initial value to the filtered intermediate delta signal.
Another method of the present invention efficiently processes a discrete time input signal, having a plurality of input signal samples that occur at a first clock rate into a discrete time output signal having a second clock rate that is R times the first clock rate. This method includes receiving the input signal, and filtering the input signal with an N-taps finite impulse response (FIR) filter having N filter coefficients in an efficient manner that takes advantage of a xe2x80x9czero paddingxe2x80x9d operation.
The present invention advantageously enables interpolation and filtering functions to be performed with a minimum number of processor operations. Furthermore the present invention advantageously provides accurate signal processing results. These techniques are applicable in many different applications, such as process control.